Optical neural network system

ABSTRACT

An optical system of an optical neural network model for parallel data processing is disclosed. Taking advantage of the fact that an auto-correlation matrix is symmetric with respect to a main diagonal and the weights for modulating the values of diagonals of the auto-correlation matrix are equal to each other, the configuration of an optical modulation unit is simplified by a one-dimensional modulation array on the one hand, and both positive and negative weights are capable of being computed at the same time on the other hand. In particular, the optical system makes up a second-order neural network exhibiting invariant characteristics against the translation and scale.

BACKGROUND OF THE INVENTION

The present invention relates to an optical system of an optical neuralnetwork model for parallel data processing.

The output y_(i) of a second-order neural network where all inputs areconnected in pairs, is given by ##EQU1## where x_(j), x_(k) are the sameinput vector of length N, w_(ijk) is a weight matrix, and F_(Th) is athreshold function. When w_(ijk) values are suitably adjusted during atraining stage, then the binary output y_(i) can differentiate betweentwo possible input classes. The equation (1) is disclosed in AppliedOptics, Vol. 26, No. 23, pp 4972-4978, (1987).

This system can be made invariant to a functional transformation of theinput by imposing certain conditions on the weight matrix w_(ijk), whichreflect the symmetry of the particular transformation. The case ofinvariance to the geometric operations of scaling and translation may beachieved by the condition that

    w.sub.ijk =w.sub.ij'k' if j-k=j'-k'                        (2)

Thus all elements of the set x_(j) x_(k) where j-k=constant aremultiplied by the same weight.

A general scheme for optical implementation of this model has beenoutlined previously. Particular optical architectures for calculation ofthe auto-correlation matrix have also been described previously, inApplied Optics, Vol. 21, No. 12, pp 2089-2090, (1982). However, thesearchitectures are complex.

SUMMARY OF THE INVENTION

The auto-correlation matrix x_(j) x_(k) with a four-element input vectoras an example and the related weight will be explained with reference toFIG. 2. In the auto-correlation matrix x_(j) x_(k) satisfying theconditions of equation (2), the direction specified by the element j-k=0is used as a diagonal, and in particular, the diagonal along thedirection specified by the element j-k=0 is assumed to be a maindiagonal. Also, the element of each diagonal is represented by the onedefined by each oblique line shown in FIG. 2, with all diagonals havingan equal weight value. FIG. 2 further shows the symmetry of thisauto-correlation matrix.

The object of the present invention is to provide an optical system withan optical configuration thereof capable of being simplified by the useof the fact that each diagonal of a weight matrix has the same value andthat the auto-correlation matrix is symmetric with respect to the maindiagonal, in which both the positive and negative weights are capable ofbeing computed at the same time, or more in particular, to provide anoptical system configuring a second-order neural network remaininginvariant with the translation and scale.

According to the present invention, there is provided an optical systemtaking advantage of the fact that the weight value of each diagonal of aauto-correlation matrix is equal and that the auto-correlation matrix issymmetric with respect to the main diagonal, comprising a firstmodulation unit for producing a vector product (auto-correlation matrix)of the very input, a second modulation unit for multiplying each term ofa matrix obtained by a related weight, and a detection unit forproducing the total of the terms on both sides of the main diagonal ofthe auto-correlation matrix.

According to a first aspect of the present invention, the firstmodulation unit, which has the function of modulating the light inaccordance with an input signal to produce an auto-correlation matrixsymmetric with respect to a main diagonal, includes a pair of modulationarrays arranged at right angles to each other. The first modulation unitmay alternatively be configured of a one-dimensional linear light sourcearray and a modulator arranged at right angles thereto.

According to a second aspect of the present invention, the secondmodulation unit includes a focus optical system for focusing the outputlight of the first modulation unit along the direction perpendicular tothe main diagonal of the auto-correlation matrix and a one-dimensionalmodulation array for modulating the light focused by the focus opticalsystem in accordance with weights. The second modulation unit mayalternatively be configured of a plurality of light sources arranged inpredetermined directions for producing the intensity-modulated light inaccordance with weights. Such light sources are preferably aone-dimensional array arranged in the direction perpendicular to themain diagonal of the auto-correlation matrix or a surface light-emittingarray having a plurality of lines for separating a light-emitting regionalong a direction parallel to the main diagonal.

According to a third aspect of the present invention, the detection unitincludes a photodetector for producing the inner product of the elementson the main diagonal of the auto-correlation matrix, which inner-productoutput may be used for error monitoring or threshold control.

In an optical system according to the present invention capable ofexhibiting invariant characteristics against the translation and scale,the weight matrix may be configured of a one-dimensional modulationarray by utilizing the fact that the weight values of the respectivediagonals of an auto-correlation matrix are equal to each other, therebysimplifying the optical configuration for weight multiplication.Further, if the symmetry of the required information (input vector) withrespect to the main diagonal of the auto-correlation matrix is usedappropriately, it is possible to divide the matrix into two matrix datawith respect to the main diagonal and multiply both the positive andnegative weights at the same time.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view showing an optical system according to an exemplaryembodiment of the present invention.

FIG. 2 is an example of the auto-correlation matrix and associatedweight matrix diagonal symmetry.

FIG. 3 is a view showing a variant embodiment of the optical systemillustrated in FIG. 1.

FIG. 4 is a view showing a variant embodiment of the optical systemwhereby multiple discrimination is possible.

FIG. 5 is a view showing a further preferred embodiment of theinvention.

FIG. 6 is a view showing a variant embodiment of the optical systemillustrated in FIG. 5.

FIG. 7 is a view showing a variant embodiment wherein the device of FIG.6 is made more compact.

FIG. 8 is a view showing three dimentional integration of the devices inFIG. 7.

FIG. 9 is a view showing a variant embodiment regarding a reflectiongeometry.

FIG. 10 is a view showing a variant embodiment regarding 90° rotation.

FIG. 11 is a view showing an example in FIG. 10.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 shows an embodiment of a general optical system aligned along anoptical axis 1. Light from a source 0 is collimated by a lens L1 toprovide uniform illumination of a pair of crossed binary transmissionmodulators M1 and M2. The modulators M1 and M2 comprises N addressablestrips, who's transmission may be varied between a high and a low state.The number of elements N is equal to the number of elements of the inputvector. The modulators M1 and M2 may be addressed by a number ofpossible means, such as electrically addressable electro-optic devicesor optically addressable bistable devices, for example. The input vectoris fed to both M1 and M2 and their combined transmission gives a realimage, R, of the outer product of the input vector with itself, which isthe auto-correlation matrix. This matrix is symmetrical about the maindiagonal D. The elements of each diagonal must now be multiplied bytheir associated weights. This is achieved using a cylindrical lens C1orientated orthogonally to the main diagonal D. Such a lens can bringall the elements from each diagonal to the same focus. At the focus ofC1 is placed a modulator M3, which has a number of discrete transmissionlevels. This modulator M3 institutes the weight multiplication. Thenumber of discrete transmission levels required is determined by theparticular patterns used during training and the training rule used. Asfor modulators M1 and M2, the modulator M3 may be electrically oroptically addressed.

The symmetry of the auto-correlation matrix provides two versions of theinformation required for a second order network, one to either side ofthe main diagonal D by the modulator M3. The dual versions are used toinstitute simultaneous calculation of positive and negative weights. Ifa weight is greater than zero, it is applied to the element of themodulator M3 addressing the + side of the matrix R, and a zero appliedto the equivalent element addressing the - side of R. If a weight isnegative, it is applied to the element addressing the - side of R, andzero applied to the equivalent element addressing the + side of R. Sincethere are N-1 independent diagonals, and thus weights, on each side ofthe main diagonal, (the main diagonal is not required) the modulator M3must contain 2N-2 addressable elements to implement both positive andnegative weights. After modulation by M3 the resulting light matrix mustbe summed. This is achieved by lens L2. All the light from the + side ofthe matrix is focused to photodetector PD1, and all the light from the -side of the matrix is focused to photodetector PD2. PD1 and PD2 provideelectrical output proportional the total light intensity in each sectorof the weighted matrix. The required summation is achieved by combiningthe outputs of both photodetectors in a differential amplifier DA. Theoutput of the differential amplifier DA is then thresholded in a deviceTH to give a binary output Z, which indicates the class of the inputwith respect to the two training examples.

An additional feature of this system is that the main diagonal, which isnot required for the primary function, provides the individual terms ofthe vector inner (scaler) product with itself. The summation of theseterms may be monitored by a third photodetector PD3 suitably positionedbetween PD1 and PD2. For the binary input of this system the output ofPD3 is the sum of non-zero terms in the input vector and may be used forerror monitoring or variable control of the threshold device TH.

A feature of this optical system is that a real image of theauto-correlation matrix is produced. FIG. 3 shows a variation on theoptical system of FIG. 1 where the real image of the auto-correlation Ris produced in an alternative fashion. A linear light source array LA,of N elements, such as a light emitting diode (LED) or laser diode (LD)array, is modulated in a binary fashion with the input vector. Naturaldivergence and a cylindrical lens C2 are used to smear the output ofarray LA across an orthogonal binary transmission modulator linear arrayM4. If the natural divergence of the individual light sources in thearray LA is insufficient to fully illuminate M4, a second orthogonalcylindrical lens crossed to the cylindrical lens C2 may be required. Themodulator M4 should have the same transmission characteristics asdescribed for M1 and M2 of FIG. 1. M4 is also modulated with the sameinput vector as the input vector regarding the modulation of LA. Thiscombination will yield a real image of the auto-correlation matrix R.Thereafter the system is as described for FIG. 1. Further alternativevariations of this scheme where the modulation of the input vector isachieved by acousto-optic modulators or other electro-optic devices canbe envisaged.

The invention, as described above, is capable of discriminating betweentwo classes only, since the system as described has only a single binaryoutput. For a system with M binary output modes, it is possible todiscriminate between 2^(M) possible classes. Such a variation of theinvention is illustrated in FIG. 4. A real image of the auto-correlationmatrix is produced as previously described. It may be necessary tointroduce a diffusing screen at the position indicated for the realimage R in FIG. 4. Rather than a single cylindrical lens and modulatorcombination, as described previously, an array of cylindrical lens' andmulti-valued modulators, all oriented at 45°, are used to feed to Mseparate photodetector pairs in a photodetector array PDA via a lens L2.Each photodetector pair of the array receives light from half of thetotal matrix, and is connected to electronics, the individualsub-systems are as disclosed in FIGS. 1 and 3. Each cylindricallens/modulator/photodetector pair combination can perform a singlebinary discrimination. The combination of M binary outputs allowsdiscrimination between 2^(M) classes.

A drawback with the schemes described above is that the transmissionmodulation device M3 or the elements constituting the array LA used forthe weight multiplication, requires many discrete transmission states(gradation displaying). This produces certain technical difficulties, asmost transmission modulation devices are optimized for binary behavior.An alternative preferred embodiment of the invention which avoids theneed for such a device is shown in FIG. 5. A pair of crossed modulatorsM1 and M2, as described in FIG. 1, are used to provide theauto-correlation. Rather than the uniform illumination described forFIG. 1 the diagonals of the combined transmission of M1 and M2 areindividually illuminated. This is achieved using a linear array of 2N-2light sources LA, orientated at 45° to the modulators, and orthogonal tothe principle diagonal of the auto-correlation matrix. The light fromeach individual light source is collimated into a strip using acylindrical lens array CA to provide 2N-2 light strips, F(1) to F(2N-2),which illuminate the individual diagonals. The weight multiplication foreach diagonal is achieved by suitable modulation of the light outputintensity of each individual light source. The choice of 2N-2 lightsources allows institution of positive and negative weights as describedpreviously. The image P transmitted by M2 is the auto-correlation matrixmultiplied by the associated weights. This is summed by lens L2, imagedto photodetectors PD1 and PD2, differentially amplified and thresholdedas before. By providing uniform unmodulated illumination of the maindiagonal the inner product sum of the input vector with itself may becollected at a third photodetector PD3 as described previously.

FIG. 6 shows a variant embodiment of the optical scheme of FIG. 5. Theindividual light source LA and cylindrical lens CA array of FIG. 5produce certain difficulties of uniformity of illumination andintegration. In FIG. 6 a device comprising a flat, surface-emittingdiagonal array of individually addressable light sources DA is shown.Such a device could comprise LED or LD integrated surface-emittingstrips. These provide the individual illumination of each diagonal.Thereafter the system is as described for FIG. 5.

For making the device of FIG. 6 more compact, a whole device of FIG. 7has photodetectors PD4, PD5 and PD6. In the whole device of FIG. 7, DA,M2, M1, PD4, PD5 and PD6 is formed as a plane device. As shown in FIG.8, these devices are stacked up and integrated to a three-dimensionaldevice.

FIG. 9 shows a variant embodiment regarding a reflection geometry.

FIG. 10 shows a variant embodiment regarding 90° rotation. In FIG. 10, asingle modulator used twice with the image being rotated between firstand second pass, means the auto-correlation matrix can be formed usingonly one device.

FIG. 11 shows an example of FIG. 10. Numeral 99 in FIG. 10 is explainedin FIG. 11. In use, the range would be controlably positioned so as tobe exactly onto itself.

While preferred embodiments along with variations and modifications havebeen set forth for disclosing the best mode and important details,further embodiments, variations and modifications are contemplatedaccording to the broader aspects of the present invention, all as setforth in the spirit and scope of the following claims.

An optical system according to the present invention, which utilizes thefact that the weight values of respective diagonals of anauto-correlation matrix are equal to each other, has a weight matrixthereof configured of a one-dimensional modulation unit thereby tosimplify the optical configuration for weight multiplication. Inaddition, the matrix is divided into two matrix data by the maindiagonal utilizing the symmetric characteristic of the requiredinformation (input vector) with respect to the main diagonal of theauto-correlation matrix, thereby making it possible to multiply both thepositive and negative weights at the same time.

We claim:
 1. An optical system for a second-order neural networkcomprising:first modulation units for modulating light in accordancewith an input signal and producing an auto-correlation matrix symmetricwith respect to a main diagonal; a second modulation unit including afocus optical system for focusing an output light of the firstmodulation units in a direction perpendicular to the main diagonal and aone-dimensional modulation array for modulating the light focused at thefocus optical system in accordance with weights; and detection units forreceiving an output light of the second modulation unit on both sides ofthe main diagonal and converting the output light of the secondmodulation unit into a plurality of electrical signals.
 2. An opticalsystem according to claim 1, wherein the second modulation unit includesa plurality of the focus optical systems and a plurality of themodulation arrays.
 3. An optical system according to claim 1, whereinthe detection unit further includes a photodetector for producing theinner product of the elements on the main diagonal of theauto-correlation matrix.
 4. An optical system according to claim 3,wherein the output of the photodetector is used for error monitoring. 5.An optical system according to claim 3, wherein the output of thephotodetector is used for threshold control.
 6. An optical systemaccording to claim 1, wherein the first modulation unit includes aone-dimensional linear light source array and a modulator arranged inthe direction perpendicular to the one-dimensional linear light sourcearray.